During additive manufacture of components using, for example, selective laser melting, typically high residual stresses are produced which are specific to the particular components. Such residual stresses may lead to the formation of cracks during build-up of the component, or may result in component distortions during subsequent heat treatment. Residual stress analyses are typically performed using X-ray methods and/or the so-called hole-drilling method. However, with these methods, it is only possible to examine surface layers of components in a locally partially destructive manner. Moreover, the surface of the component must not be excessively curved. A method for measuring residual stresses of a component while it is being manufactured by an additive manufacturing process is described in U.S. Pat. No. 6,553,275 B1. In this method, a powder material to be melted by a laser is disposed on a substrate provided with strain gauges on its rear surface. Residual stresses arising during the manufacture of the component are determined via the elongations indirectly measured by the strain gauges.